Factorise: 6x^2 + 5x - 6 | vedclass

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Question

(A) To factorise the quadratic polynomial $6x^2 + 5x - 6$,we use the splitting the middle term method.We need to find two numbers $l$ and $m$ such tha

Vedclass · Accepted Answer

$(2x + 3)(3x - 2)$

Vedclass · Answer

(A) To factorise the quadratic polynomial $6x^2 + 5x - 6$,we use the splitting the middle term method.We need to find two numbers $l$ and $m$ such that $l + m = 5$ (the coefficient of $x$) and $lm = 6 	imes (-6) = -36$ (the product of the coefficient of $x^2$ and the constant term).We observe that $9 + (-4) = 5$ and $9 	imes (-4) = -36$.Now,rewrite the middle term $5x$ as $9x - 4x$:$6x^2 + 9x - 4x - 6$Group the terms:$(6x^2 + 9x) - (4x + 6)$Factor out the common terms from each group:$3x(2x + 3) - 2(2x + 3)$Finally,factor out the common binomial $(2x + 3)$:$(2x + 3)(3x - 2)$

Factorise: $6x^2 + 5x - 6$

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